Reversed Dickson polynomials

Abstract

We investigate fixed points and cycle types of permutation polynomials and complete permutation polynomials arising from reversed Dickson polynomials of the first kind and second kind over $\mathbb{F}_p$. We also study the permutation behaviour of reversed Dickson polynomials of the first kind and second kind over $\mathbb{Z}_m$. Moreover, we prove two special cases of a conjecture on the permutation behaviour of reversed Dickson polynomials over $\mathbb{F}_p$.